One of the most important directions in current biomedical research is the quest to understand the genetic contributions to complex diseases. A critical part of many such investigations is the use of linkage analysis to find possible disease susceptibility loci. Recently, there has been substantial interest in using linkage methods designed for quantitative phenotypes as a tool for finding genes associated with diseases. For example, this approach has been applied to dyslexia, type II diabetes, hypertension, and heart disease. This growth in interest in QTL mapping has been accompanied by a great deal of new work on statistical methods, but little of that work has dealt with selected samples, despite the fact that selected samples are arguably more common than population samples in human QTL mapping. The general aim of this grant is to develop powerful statistics for QTL mapping with selected samples, and powerful designs for selecting such samples. The specific aims are the following. 1) Extend the work of Forrest and Feingold (2000) to develop powerful composite statistics and practical sampling designs for concordant sibling pairs, combined discordant and concordant sibling pair designs, and larger pedigrees selected because of extreme trait values of two or more members. 2) Compare the performance of various test statistics for single-proband ascertainment schemes. 3) Investigate the relative power of population sampling, single-proband sampling, and multiple-proband sampling under various genetic models.